The shorter leg of a 30-60-90 triangle is 6. What is the length of the hypotenuse?
the sides are in the ratio 1:√3:2, so ...
To find the length of the hypotenuse of a 30-60-90 triangle, you can use the ratios of the sides. In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.
Since you know that the length of the shorter leg (opposite the 30-degree angle) is 6, you can set up the ratio:
1 : √3 : 2 = 6 : x : ?
To solve for x, you can use cross-multiplication:
1 * x = √3 * 6
Simplifying the right side:
x = 6√3
Therefore, the length of the hypotenuse is 6√3.